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United States Patent |
6,199,026
|
Shiraishi
,   et al.
|
March 6, 2001
|
Method of and apparatus for simulating rolling tire
Abstract
A method of simulating a rolling tire and a simulator are disclosed, the
simulating method comprises the steps of: dividing the tire into a tire
body and a tread part therearound, wherein the tire body is defined as a
toroidal part of the tire which is materially and geometrically the same
or constant along the tire circumferential direction, and the tread part
is defined as the remaining annular part around the tire body; modeling
the tire body in finite elements; modeling the tread part in finite
elements; combining the tread model with the body model to form a tire
model; adjusting the beads of the tire model to a wheel rim on which the
tire is mounted; contacting the tire model with a road model; moving the
road model at predetermined time intervals relatively to the tire model,
giving running conditions; obtaining information about the tire model as
numerical data in time sequence; and processing the numerical data in time
sequence to be outputted as a visible information. Preferably, the body
model comprises models of the bead cores, rubber parts, and cord
reinforcements each comprising a model of a cord ply and a model of
topping rubber, wherein the cord ply is modeled in quadrilateral membrane
elements defined as an orthotropic material, and the topping rubber is
modeled in hexahedral solid elements.
Inventors:
|
Shiraishi; Masaki (Kobe, JP);
Miyori; Akio (Akashi, JP)
|
Assignee:
|
Sumitomo Rubber Industries, Ltd. (Kobe, JP)
|
Appl. No.:
|
198509 |
Filed:
|
November 24, 1998 |
Foreign Application Priority Data
| Nov 25, 1997[JP] | 9-322540 |
| Jan 19, 1998[JP] | 10-007611 |
| Jan 19, 1998[JP] | 10-007612 |
Current U.S. Class: |
702/140; 703/1 |
Intern'l Class: |
G01L 025/00 |
Field of Search: |
702/140,82
703/6,8,1,3,12,7
152/548,450,454
73/146
157/13
701/27
|
References Cited
U.S. Patent Documents
5396438 | Mar., 1995 | Oblizajek | 364/552.
|
5559729 | Sep., 1996 | Abe | 364/578.
|
5710718 | Jan., 1998 | Kamewaga et al. | 364/512.
|
Primary Examiner: Hoff; Marc S.
Assistant Examiner: Raymond; Edward
Attorney, Agent or Firm: Birch, Stewart, Kolasch & Birch, LLP
Claims
What is claimed is:
1. A method of simulating a pneumatic tire rolling on a road, said
pneumatic tire comprising a carcass extending between beads, a bead core
disposed in each of the beads, a belt disposed radially outside the
carcass, a tread rubber radially outside the belt, sidewall rubbers
axially outside the carcass, and bead rubbers in the beads, the method
comprising the steps of
dividing the tire into a tire body and a tread part therearound, wherein
the tire body is defined as a toroidal part of the tire which is materially
and geometrically the same or constant along the tire circumferential
direction, and comprises the bead cores, rubber parts including the
sidewall rubbers and bead rubbers, and cord reinforcements including the
carcass and the belt, and
the tread part is defined as the remaining annular part around the tire
body which comprises at least a radially outmost part of the tread rubber,
modeling the tire body in finite elements to make a body model,
modeling the tread part in finite elements to make a tread model,
making a finite-element model of the tire by combining the tread model with
the body model,
modeling the surface of the road in finite elements to make a road model,
adjusting the beads of the tire model to a wheel rim on which the tire is
mounted,
contacting the tire model with the road model,
moving the road model at predetermined intervals relatively to the tire
model, giving running conditions including a moving speed, a slip angle, a
tire load and a tire inflation pressure,
obtaining information about the tire model at said predetermined intervals
as numerical data in time sequence, and
processing said numerical data in time sequence to be outputted as a
visible information.
2. The method according to claim 1, characterized in that said body model
comprises
models of the bead cores,
models of the rubber parts, and
models of the cord reinforcements each comprising a model of a cord ply and
a model of topping rubber, wherein the cord ply is modeled in
quadrilateral membrane elements defined as an orthotropic material, and
the topping rubber is modeled in hexahedral solid elements.
3. The method according to claim 2, characterized in that said information
is at least one of
a cornering force during cornering,
a ground pressure distribution,
a ground contacting area,
an internal stress distribution,
a reaction force from the road during running,
a vibration damping factor, and
a wear energy caused by slippage during running.
4. The method according to claim 2, characterized in that said running
conditions further include at least one of
a friction coefficient between the tire and road,
a camber angle of the tire, and
the number, shape and sizes of protrusion(s) and/or hollow(s) on the road.
5. The method according to claim 2, characterized in that said tire is
provided in the tread with grooves having a maximum depth, and said tread
part is a radially outmost part between the tread surface and a radially
inner position corresponding to the maximum depth.
6. The method according to claim 1, characterized in that said information
is at least one of
a cornering force during cornering,
a ground pressure distribution,
a ground contacting area,
an internal stress distribution,
a reaction force from the road during running,
a vibration damping factor, and
a wear energy caused by slippage during running.
7. The method according to claim 6, characterized in that said running
conditions further include at least one of
a friction coefficient between the tire and road,
a camber angle of the tire, and
the number, shape and sizes of protrusion(s) and/or hollow(s) on the road.
8. The method according to claim 6, characterized in that said tire is
provided in the tread with grooves having a maximum depth, and said tread
part is a radially outmost part between the tread surface and a radially
inner position corresponding to the maximum depth.
9. The method according to claim 1, characterized in that said running
conditions further include at least one of
a friction coefficient between the tire and road,
a camber angle of the tire, and
the number, shape and sizes of protrusion(s) and/or hollow(s) on the road.
10. The method according to claim 9, characterized in that said tire is
provided in the tread with grooves having a maximum depth, and said tread
part is a radially outmost part between the tread surface and a radially
inner position corresponding to the maximum depth.
11. The method according to claim 1, characterized in that said tire is
provided in the tread with grooves having a maximum depth, and said tread
part is a radially outmost part between the tread surface and a radially
inner position corresponding to the maximum depth.
12. An apparatus for simulating a pneumatic tire rolling on a road, which
comprises means of performing the steps as set forth in claim 1.
Description
BACKGROUND OF THE INVENTION
The present invention relates to a method of and apparatus for simulating
rolling pneumatic tires which is capable of analyzing dynamic tire
characteristics, e.g. cornering characteristics, vibration damping
characteristics, wear characteristics and the like.
Pneumatic tires have made remarkable progress in recent years. Hitherto,
such progress has been attained by patient works, repeating trial
production, running tests, investigations and improvements. Thus, it is
difficult to decrease the development cost and time.
On the other hand, recently, a finite element method becomes used to assist
tire designers in analyzing static tire characteristics, e.g.
load-deflection, with using a simplified tire model in which the tread
pattern is ignored, or regarded as a plane, and reinforcing cord layers
such as carcass and belt are regarded as a simple single shell element.
Thus, there are limits to such static simulation and simplified tire model
when utilizing in actual development of tires.
It is therefore an object of the present invention is to provide a method
of and an apparatus of simulating a rolling tire by which accurate
analysis dynamic characteristics and exact estimation of tire performances
are made possible.
SUMMARY OF THE INVENTION
According to one aspect of the present invention, a method of simulating a
pneumatic tire rolling on a road, comprises the steps of:
dividing the tire into a tire body and a tread part therearound, wherein
the tire body is defined as a toroidal part of the tire which is materially
and geometrically the same or constant along the tire circumferential
direction, and comprises bead cores, rubber parts including sidewall
rubbers and bead rubbers, and cord reinforcements including a carcass and
a belt, and
the tread part is defined as the remaining annular part around the tire
body which comprises at least a radially outmost part of a tread rubber;
modeling the tire body in finite elements to make a body model;
modeling the tread part in finite elements to make a tread model;
making a finite-element model of the tire by combining the tread model with
the body model;
modeling the surface of the road in finite elements to make a road model;
adjusting the beads of the tire model to a wheel rim on which the tire is
mounted;
contacting the tire model with the road model;
moving the road model at predetermined time intervals relatively to the
tire model, giving running conditions including a moving speed, a slip
angle, a tire load and a tire inflation pressure;
obtaining information about the tire model at the above-mentioned
predetermined intervals as numerical data in time sequence; and
processing the numerical data in time sequence to be outputted as a visible
information.
Preferably, the body model comprises models of the bead cores, models of
the rubber parts, and models of the cord reinforcements each comprising a
model of a cord ply and a model of topping rubber, wherein the cord ply is
modeled in quadrilateral membrane elements defined as an orthotropic
material, and the topping rubber is modeled in hexahedral solid elements.
BRIEF DESCRIPTION OF THE DRAWINGS
Embodiments of the present invention will now be described in detail in
conjunction with the drawings, in which:
FIG. 1 is a perspective view of a pneumatic tire showing a typical tire
structure;
FIG. 2 is a simulator output showing a perspective view of a finite-element
model of a pneumatic tire;
FIG. 3 is a simulator output showing a perspective view of a body model
thereof;
FIG. 4 is a simulator output showing a perspective view of a tread model
thereof;
FIG. 5 is a diagram for explaining a model of a rubberized cord ply;
FIG. 6 is a diagram showing deformation of the elements along the boundary
between the tire body model and tread model;
FIG. 7 is a block diagram for explaining a dynamic tire simulator according
to the present invention;
FIG. 8 is an example of the system flowchart of the simulator;
FIG. 9 is a simulator output showing a cross sectional view showing a
loaded state of the tire model;
FIG. 10 is a simulator output showing the tire model during cornering;
FIG. 11 is a simulator output showing variations of initial cornering force
computed;
FIG. 12 is a simulator output showing a ground pressure distribution during
cornering;
FIG. 13 is a simulator output showing the cross section of the tire model
during cornering;
FIG. 14 is a diagram for explaining a cornering force;
FIG. 15A is a simulator output showing a perspective view showing one scene
of the tire model running on an uneven road surface;
FIG. 15B is an enlarged view of a finite-element model of a protrusion on
the uneven road;
FIG. 16 is a simulator output showing a side view of the tire model just
getting over the protrusion;
FIG. 17 is a simulator output showing damping characteristics (reactive
forces when getting over the protrusion);
FIG. 18 is a simulator output showing a distribution of tread wear energy
obtained during the cornering simulation; and
FIG. 19 is a graph showing the wear energy obtained by simulation and
experiments.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
Referring to FIG. 1 in which a radial tire for passenger cars is shown as a
typical example of pneumatic tires, a tire structure is first described.
Typical Tire Structure
A tire T comprises a tread 12, a pair of sidewalls 13 and a pair of axially
spaced beads 14 to have a toroidal shape. The tire T is provided with a
carcass 16 as the main frame, which extends from one of the beads 14 to
the other through the tread 12 and sidewalls 13. The tread 12 is
reinforced with a belt 17, 19 disposed on the radially outside of the
carcass 16. Further, each bead 14 is provided with a bead core 15 disposed
therein to be secured on the wheel rim, and optionally a reinforcing cord
layer disposed along the carcass 16. The carcass 16, belt 17, 19 and
optional reinforcing cord layer collectively form a reinforcing-cord
structure (hereinafter cord-reinforcement F). On both sides of the
cord-reinforcement F, there are disposed many kinds of rubber strips: a
tread rubber 20 and sidewall rubber 21 on the outside, a bead rubber 22
extending from the outside to the inside, and an inner liner rubber on the
inside. Further, between the carcass turnup and main portion, a hard bead
apex rubber is disposed. On the tread rubber 20, tread grooves G1, G2 are
formed to define a tread pattern.
In the example shown in FIG. 1, the carcass 16 is composed of a single ply
16a of organic (polyester) fiber cords arranged radially at substantially
90 degrees with respect to the tire circumferential direction and turned
up around the bead cores 15. The belt is composed of a breaker 17 disposed
on the radially outside of the carcass 16 and a band 19 disposed on the
radially outside of the breaker 17. The breaker 17 is composed of two
cross plies 17A and 17B of parallel steel cords laid at 20 degrees with
respect to the circumferential direction. The band 19 is composed of a
pair of axially spaced edge plies and a cut-end full-width ply disposed
thereon, each made of nylon cords laid substantially parallel to the
circumferential direction. The tread rubber 20 has a double-layered
structure comprising an under-tread rubber 20a between the belt and a
tread groove bottom line and a cap rubber 20b disposed thereon. The
sidewall rubber 21 is smaller in the complex elastic modulus than the
tread rubber 20. The bead rubber 22 has a relatively higher elastic
modulus than others. The tread 12 is provided with circumferential grooves
G1 and axial groove G2 to form a bi-directional tread pattern.
Summary of Simulations
In this invention, various dynamic simulations are made based on a finite
element method.
The tire is first modeled by finite elements, giving various boundary
conditions, e.g. shapes of elements, material characteristics and the
like, and kinetic equations are solved by means of a computer.
To solve the kinetic equations, known computational algorithm may be used.
In this example, an explicit method (YOUKAIHO) is used. For example, mass
matrix M, stiffness matrix K, damping matrix C of the elements are first
defined by the elements' shapes and material characteristics, e.g.
density, Young's modulus, damping factor and the like.
These matrixes are combined to define the matrix of the entire system to be
simulated, and further, applying boundary conditions, the following
kinetic equation (Eq.1) is defined.
F=Mx+Cx+Kx
wherein
F=external force matrix
M=mass matrix
x=acceleration matrix
C=damping matrix
x=velocity matrix
K=stiffness matrix
x=displacement matrix
To make various dynamic simulations, this equation is computed to find the
solutions at predetermined short time intervals (t). Preferably, the time
intervals (t) is set to being not more than 0.9 times the minimum of the
transfer time of stress wave computed on every elements.
Modeling
The subject tire T is modeled by different types of elements (2a, 2b, 2c -
- - ) suitable for each individual part or member. For example,
three-dimensional (3-D) elements, e.g. tetrahedral element, pentahedral
element and hexahedral element and two-dimensional (2-D) elements, e.g. a
quadrilateral element are used.
As shown in FIGS. 2, 3 and 4, a finite-element model 2 of the tire T is
made up of a body model 3 and a tread model 4 which are separately modeled
and then join with each other.
The body model 3 is defined as of a tire body 1B or an annular part of the
tire which is materially and geometrically the same or constant along the
tire circumferential direction.
The tread model 4 is therefore, defined as the remaining part (hereinafter
tread part 1A) around the tire body 1B which varies along the tire
circumferential direction either materially or geometrically at least.
As a result, it is possible to use relatively large-sized elements in the
tire body model 3 in comparison with the tread model 4, whereby the
computing time can be greatly saved without degrading the simulation.
Body model
As shown in FIGS. 3 and 13, the tire body 1B is modeled by plural kinds of
elements suitable for each individual part or member.
In case of the example tire T, the tire body model 3 is made up of rubber
models of various rubbers such as the tread rubber, sidewall rubber, bead
rubber and the like, and a bead core model, and cord ply models of various
reinforcing cord plies such as the carcass ply, belt plies and the like.
Cord ply model
As shown in FIG. 5, an actual reinforcing cord ply is such that parallel
cords (c) are rubberized with topping rubber (t). Therefore, a ply of
cords (c) is modeled by quadrilateral membrane elements (5a, 5b), and a
layer of topping rubber (t) is modeled by hexahedral solid elements (5c,
5d, 5e).
The quadrilateral membrane elements for such a cord ply are defined as an
orthotropic material in which the rigidity in the cord longitudinal
direction differs from the rigidity in the normal direction thereto and
the rigidity in each direction is homogeneous, and the thickness thereof
is the same as the cord diameter.
The hexahedral solid elements for such a topping rubber layer are defined
as a homogeneous super-viscoelastic material.
Rubber model
The sidewall rubber 21, bead rubber 22, a part of the tread rubber (in this
example, only the under-tread rubber 10a), and other rubber layers (if
any) are modeled by a hexahedral solid element and/or a pentahedral solid
element. As to the material definition, the elements are defined as a
homogeneous viscoelastic material whose complex elastic modulus is the
same as the actual rubber.
Bead core model
The bead core 14 is modeled by a hexahedral solid element and/or a
pentahedral solid element. As to the material definition, the elements are
defined as a relatively rigid material having an elastic modulus equal to
the actual bead core.
Tread model
The tread model 4 is of a radially outmost part 1A of the tire which varies
materially and/or geometrically in the circumferential direction as
explained above. However, this does not intend to completely exclude a
circumferentially homogeneous part. A circumferentially homogeneous part
immediately inside the tread pattern may be included like a pedestal. For
example, it may be possible to define the radially outmost part 1A as
being the entire tread rubber outside the belt. In case of the example
tire T, it is also possible to define the tread model 4 as of the tread
cap rubber 20b, and accordingly the tire body 1B is the remaining part
other than the tread cap rubber 20b.
In any way, the tread part 1A is modeled by tetrahedral solid elements (4a,
4b - - - ) in full detail all around the tire as shown in FIG. 4. The
tetrahedral solid elements are defined as a homogeneous viscoelastic
material whose complex elastic modulus is the same as the actual rubber.
Because it is preferable to minimize such a circumferentially homogeneous
part immediately inside the tread pattern, the tread model 4 is usually
formed as of a mix of various shapes of rubber pieces such as blocks,
ribs, lugs and the like.
Tire model
As explained above, the tread model 4 is formed separately from the body
model 3. Then, to form a tire model 2, the tread model 4 is connected with
the body model 3 by means of forced displacement such that the elements'
faces and nodes on the radially inside of the tread model 4 do not change
their relative positions to the elements' faces and nodes on the radially
outside of the body model 3 anytime as shown in FIG. 6.
Road model
FIG. 10 shows a model of an even road surface 7, wherein the road surface
is modeled by quadrilateral (rectangle) rigid elements.
FIGS. 15A and 15B show a model of a bumpy road surface, wherein the flat
part 7 and the remaining part 8 are both modeled by quadrilateral rigid
elements. In FIG. 15B, a protrusion 8 which is a half-columnar protrusion
whose radius is 1 cm is modeled by quadrilateral rigid elements (8, 8a,
8b, 8c - - - ).
By varying the friction coefficient of the simulated road surface, various
conditions such as snowy road, icy road, sandy road, mudy road and the
like can be simulated.
Simulator
As shown in FIG. 7, the simulator according to the present invention
includes a computer comprising a CPU, ROM, RAM, and I/O ports which are
connected with data bus. Further, the simulator includes peripherals
connected to the I/O ports, such as input devices (I), e.g. keyboard,
mouse and the like, output devices (O), e.g. display and printer, external
memory (D), e.g. hard disk, magneto-optic disk and the like. According to
a program stored in the memory (D), the computer plays the following
multiple functions. In FIG. 8, an example of the system flowchart is
shown.
Making Body model
As explained above, the tire body 1B is defined as being uniform all around
the tire axis. Therefore, the above-mentioned 3-D body model 3 is made by
inputting two dimensional (2-D) data of the tire cross section, and
spreading the inputted 2-D data in the circumferential direction.
In the simulator therefore, the contours of various parts, e.g. carcass
plies, belt plies, bead cores, bead apex rubber, bead rubber, sidewall
rubber, under tread rubber and the like are first inputted as 2-D data.
The inputted 2-D data can be shown on the display monitor as a 2-D wire
frame model for the purpose of confirmation and the like. It is possible
to input the date by means of keyboard, mouse, scanner, digitizer and the
like. Then, the 2-D frame model is spread around the tire axis to make a
toroidal 3-D solid model, and at the same time, the solid model is divided
into finite elements (tetrahedral elements, pentahedral elements and
hexahedral elements, quadrilateral elements and the like) as explained
above.
Making Tread model
As explained above, the tread part 1A is usually not uniform in the
circumferential direction. On the other hand, a tread pattern is usually
formed by repeating a design unit in the tire circumferential direction.
In the simulator, therefore, in order to save the data input, 3-D data of
one design unit are inputted, and they are repeated in the circumferential
direction to form a complete tread pattern.
To further simplify the input data, it is preferable to define the
above-mentioned tread part 1A as being materially and geometrically the
same or constant along the radial direction if possible. In this case, the
simulator spreads radially of the tire 2-D data of the design unit at the
tread face for example to form the 3-D model of the design unit which is
to be circumferentially repeated.
In anyway, when a 3-D solid model of the tread part 1A is made, the
simulator divides it into finite elements (tetrahedral elements) as
explained above.
Up to this point, all geometrical data of the tire are inputted. Further,
material data are inputted. When the body model, tread model and
intervening models such as of one design unit are made, the data thereof
are stored in a library prepared in a memory (D) for reuse.
The operator can select a body model and a tread model from the library,
and in response to the operator's demand, the simulator joins the tread
model 4 to the body model 3 to make a tire model 2.
Rim-mounting and Inflating simulation
Actual pneumatic tires must be mounted on a wheel rim and inflated with
air. In the simulation, however, it is not necessary to model the wheel
rim because it is regarded as an almost complete rigid body in comparison
with the tire.
Therefore, to simulate the tire mounted on a wheel rim, as shown in FIG. 9,
the axial distance W between the beads of the tire model 2 is set up to at
a constant value equal to the rim width.--Usually the bead width W of a
pneumatic tire not mounted on a wheel rim is larger than the rim width.
Thus, by mounting the tire, the width W decreases. At the same time, a
surface 10 of the beads which comes to contact with the wheel rim is
restrained. In other words, the rim-contacting face 10 is maintained not
to change the relative position with respect to the direction of the tire
axis CL and the normal direction (r) to the tire axis or radial direction.
In the simulator, according to the tire size inputted, the simulator
searches a tire-rim database stored in the memory (D) for an approved rim
size. If not found, the simulator requests the operator to choose one rim
from a list or to input new data of the wheel rim. Then, according to the
rim data chosen or inputted, the simulator computes the rim-contacting
surface 10, and restrain the surface 10 not to change axially and radially
their coordinates relative to the tire axis. However, to simulate the
rotation, the motion in the circumferential direction is allowed.
Thus, the tire model can simulate its state mounted on a wheel rim.
Further, to simulate the inflation of the tire, the simulator applies a
load or strain of a constant value corresponding to the inner pressure of
the tire to the inner surface of the tire model 2.
Making Road model
The simulator makes a road model using quadrilateral rigid elements
according to the inputted road surface data. As to the road surface data,
the friction coefficient of the road surface must be inputted together
with conditions of the road surface, for example, whether smooth or bumpy,
the shape, size and number of protrusion(s) and/or hollow(s) if bumpy, an
angle of inclination and so on.
Dynamic Simulation of Rolling Tire
To simulate a pneumatic tire rolling on a road, the tire model is caused to
contact with a road model and a tire load is applied thereto. Then, the
road surface is moved relative to the tire in predetermined conditions if
the tire is on an idler wheel. If the tire is on a drive wheel, the tire
is rotated. As the running condition data, whether straight running or
cornering, i.e. slip angle, and the running speed, camber angle, tire
load, air pressure and the like are inputted. According to the inputted
data, the simulator makes the above-mentioned matrixes and kinetic
equation and computes the equation to find solutions at the predetermined
time intervals. These solutions are once stored in the hard disk memory
(D), and in response to the operator's demand, the simulator outputs these
to the display as an animation or to the printer as still pictures.
Cornering simulation
To simulate a tire during cornering, the road surface is moved relatively
to the tire in a direction at a certain angle .alpha. with respect to the
longitudinal direction of the tire as shown in FIG. 10, wherein the angle
.alpha. corresponds to the slip angle of the tire shown in FIG. 14. FIG.
10 is a copy of the display monitor showing a cornering simulation. As
shown in FIG. 14, during cornering, a ground contacting part of the tread
is moved sideways as the tire rotates while contacting with the road
surface. Accordingly, the tread rubber undergoes a sharing deformation
thereby causing a force at a right angle to the traveling direction,
namely cornering force.
In the cornering simulation, the simulator computes and outputs the
cornering force and ground pressure distribution and the internal stress
distribution of the tire.
FIG. 11 is a simulator output showing the cornering force obtained from a
cornering simulation as a function of the lapse time from the start. In
this simulation, the road surface was defined as a flat and rigid surface
and modeled as explained above. The tire model inflated to a normal
pressure, and the road surface model was pressed on the tread by a
standard tire load. The tire model was rotatable around the axis, and was
rotated by the frictional force of the moving road surface. Both the
static and dynamic friction coefficients were 1.0. The moving speed was 20
km/h. The cornering force from the simulation well corresponds to
experimental results of a tire drum test on which results are also shown
on the right-hand side of FIG. 11.
From the simulation, it was discovered that the cornering force becomes a
stationary state after 0.15 to 0.20 sec. which corresponding to about one
half rotation of the tire. Accordingly, it is almost impossible to
estimate the cornering force without the dynamic simulation in which the
tire model is rotated at least one half revolution.
Further, this simulation was carried out at the slip angle .alpha. of zero
degree. Thus, it was a straight running simulation. However, a small
cornering force was observed as shown in FIG. 11, which is supposed to be
ply steer of the belt plies. This shows that the simulation is a true
simulation.
FIG. 12 is a simulator output showing the ground pressure distribution
during cornering at the slip angle of 4 degrees. In FIG. 12, only the
highest pressure regions are shaded with fine dots, but in the actual
output, the distribution is indicated by changing color.
FIG. 13 is a simulator output showing the cross section of the tire in the
circumferential center of the ground contacting patch during cornering at
the slip angle of 4 degrees. In FIG. 13, the highest stress regions are
shaded with fine dots, but in the actual output, the stress distribution
is indicated by changing color. FIG. 13 shows that the simulator can
reproduce a state in which a large tensile stress is occurring in the
inside tire sidewall (right-hand side of FIG. 13).
Tread Wear Estimation
It can be said that the amount of wear is proportional to wear energy. The
wear energy at a specific point is obtained by integrating the product of
the ground pressure and slippage at the point from touching to the road
surface to detaching therefrom.
In this invention, therefore, with regard to every node of the elements in
the ground contacting region, a wear energy in X-axis direction (tire
axial direction) is calculated by integrating the product of the sharing
force and slippage in X-axis direction and also a wear energy in Y-axis
direction (tire circumferential direction) is calculated by integrating
the product of the sharing force and slippage in Y-axis direction. Then
these are added up as the overall wear energy at the node.
The simulator makes such calculations during making a running simulation.
When the calculations are finished, the simulator stores the results in
the memory (D), and then in response to an operator's demand, the
simulator outputs the results to the display monitor or the printer.
FIG. 18 shows such an output, wherein the wear energy distribution is
indicated on the tread model 4 by changing color although the color
becomes a monotone in FIG. 18. This output example was obtained during the
above-mentioned cornering simulation. Of course, it is possible to compute
the wear energy under various conditions including straight running.
FIG. 19 shows the wear energy obtained by the simulation and that by
experiments. This shows that the method and simulator of the present
invention well simulate the actual running conditions, and that the tread
wear estimation is reliable.
In this invention, it is also possible to compute such overall wear energy
for a specific small area, for example, only one block or rib.
Damping Simulation (Vibrational Characteristic Estimation)
In a damping simulation, road data of a bumpy road are inputted to the
simulator to make a bumpy road model. The tire model 2 was mounted on a
wheel rim and inflated to a pressure as explained above, and the tire
model 2 was placed on the road model and loaded by applying a standard
load to the tire axis CL. Then the road surface 7 was moved at a
predetermined speed (60 km/h) to rotate the tire by the frictional force
between them. The dynamic and static friction coefficients were 1.0 in the
following test simulation.
The simulator computes the reaction force to the tire axis in the vertical
direction and traveling direction in sequence of running time. The results
are once stored in the memory (D), and then in response to an operator's
demand, the simulator outputs the results to the display monitor or the
printer.
FIG. 15A is a copy of one scene of the animated running simulation in which
a protrusion 8 traverses the traveling course. The modeling of such a road
is carried out automatically by the apparatus based on the inputted data
as explained above.
FIG. 16 is also a copy of one scene which shows the tire model just running
over the protrusion. In the actual output, the stress distribution
obtained by computing the stress at every node is also shown by changing
color.
FIG. 17 is a simulator output (graph) in which the above-mentioned reaction
force in two directions are shown in time sequence. Thus, the vibration
characteristics such as damping factor are quite obvious therefrom. In
FIG. 17, experimental results are also shown in broken line, from which it
is known that the method and simulator of the present invention well
simulate the actual running conditions on bumpy roads and that the
estimate of the damping characteristic is reliable.
Foot print
As explained above, the simulator can compute the ground pressure
distribution under various running conditions, and the data thereof is
stored. Using those data, the simulator can output only a part of the
tread of which ground pressure is positive, as the foot print during
running.
The tire model which was used in the above-mentioned test simulations and
is shown in FIG. 2 has 76359 elements and 43896 nodes. The modeled tire is
a 235/45ZR17LM602 passenger car tire of Sumitomo Rubber Ind., Ltd.
As explained above, in the present invention, it is possible to make
accurate simulations of a rolling tire under various conditions and also
reliable estimations of the tire characteristics and performances.
Further, it may be possible to estimate or analyze wet performances such
as aquaplaning performance by coupling with fluid.
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